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Statistically Recognize Faces Based on Hidden Markov Models

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### Statistically Recognize Faces Based on Hidden Markov Models

### What is Hidden Markov Model?

Presented by

Timothy Hsiao-Yi Chin

Rahul Mody

E6886 Project

Its underlying is a Markov Chain.

An HMM, at each unit of time, a single observation is generated from the current state according to the probability distribution, which is dependent on this state.

E6886 Project

Mathematical Notation of HMM

- Suppose that there are T states {S1, …, ST} and the probability between state i and j is Pij. Observation of system can be defined as ot at time t. Let bSi(oi) be the probability function of ot at time t. Lastly, we have the initial probability , i = 1, …, n of Markov chain. Then the likelihood of the observing the sequence o is

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Which probability function of ot?

- In HMM framework, observation o is assumed to be governed by the density of a Gaussian mixture distribution.
- Where k is the dimension of ot, and where oiand

are the mean vector and covariance matrix, respectively

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Re-estimation of mean, covariances, and the transition probabilities

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Represent it as a Markov Model*

- States:
- State transition probabilities:
- Initial state distribution:

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What is sequence o in this example?*

- Sequence o:
- The probability could be computed by the conditional probability:

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What other parameters will be needed?

- If we can not see what is inside blue circle, what can we actually see?
- Observations:
- Observation probabilities:

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Forward-Backward Algorithm: Backward

- If there is a
- Then
- The Forward-Backward Algorithm tells us that
- for any time t

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Face identification using HMM

- An Observation sequence is extracted from the unknown face, the likelihood of each HMM generating this face could be computed.
- In theory, the likelihood is
- The maximum P(O) can identifies the unknown faces.
- However, it takes too much time to compute.

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Face identification using HMM

- In practice, we only need one S sequence

which maximizes

- This is a dynamic programming optimization procedure.

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Viterbi Algorithm

- Given a S sequence, a dynamic programming approach to solve this problem
- where
- By induction, the max Probability in state i+1 at time t+1 is based on the max probability in state I at time t.

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Algorithm itself

- Initialization

where denotes the collection of that sequence which is based on max

- Recursion:

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So far we have this block diagram

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Face Detection

- In simple face recognition framework, the picture is assumed to be a frontal view of a single person and the background is monochrome.
- This project assumes that with the techniques of face detection, the performance of face recognition may be better than the approach presented above.

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Acknowledgement

- The authors of this presentation slides would like to give thanks to Dr. Doan, UIUC.

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Reference

- [1] Ferdinando Samaria, and Steve Young, HMM-based architecture for face identification.
- [2] Jia, Li, Amir Najmi, and Robert M. Gray, Image Classification by a Two-Dimensional Hidden Markov Model
- [3] Ming-Hsuan Yang, David J. Kriegman, Narendra Ahuja, Detecting Faces In Images: A survey
- [4] T.K. Leung, M. C. Burl, and P. Perona, Finding Faces in Cluttered Scenes using Random Labeled Graph Matching
- [5] James Wayman, Anil Jain, Davide Maltoni, and Dario Maio, Biometric Systems, Springer, 2005

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